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Simplifying 9x2 + -0.6x + 0.01 = 0 Reorder the terms: 0.01 + -0.6x + 9x2 = 0 Solving 0.01 + -0.6x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.001111111111 + -0.06666666667x + x2 = 0 Move the constant term to the right: Add '-0.001111111111' to each side of the equation. 0.001111111111 + -0.06666666667x + -0.001111111111 + x2 = 0 + -0.001111111111 Reorder the terms: 0.001111111111 + -0.001111111111 + -0.06666666667x + x2 = 0 + -0.001111111111 Combine like terms: 0.001111111111 + -0.001111111111 = 0.000000000000 0.000000000000 + -0.06666666667x + x2 = 0 + -0.001111111111 -0.06666666667x + x2 = 0 + -0.001111111111 Combine like terms: 0 + -0.001111111111 = -0.001111111111 -0.06666666667x + x2 = -0.001111111111 The x term is -0.06666666667x. Take half its coefficient (-0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. -0.06666666667x + 0.001111111112 + x2 = -0.001111111111 + 0.001111111112 Reorder the terms: 0.001111111112 + -0.06666666667x + x2 = -0.001111111111 + 0.001111111112 Combine like terms: -0.001111111111 + 0.001111111112 = 0.000000000001 0.001111111112 + -0.06666666667x + x2 = 0.000000000001 Factor a perfect square on the left side: (x + -0.03333333334)(x + -0.03333333334) = 0.000000000001 Calculate the square root of the right side: 0.000001 Break this problem into two subproblems by setting (x + -0.03333333334) equal to 0.000001 and -0.000001.Subproblem 1
x + -0.03333333334 = 0.000001 Simplifying x + -0.03333333334 = 0.000001 Reorder the terms: -0.03333333334 + x = 0.000001 Solving -0.03333333334 + x = 0.000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = 0.000001 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = 0.000001 + 0.03333333334 x = 0.000001 + 0.03333333334 Combine like terms: 0.000001 + 0.03333333334 = 0.03333433334 x = 0.03333433334 Simplifying x = 0.03333433334Subproblem 2
x + -0.03333333334 = -0.000001 Simplifying x + -0.03333333334 = -0.000001 Reorder the terms: -0.03333333334 + x = -0.000001 Solving -0.03333333334 + x = -0.000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03333333334' to each side of the equation. -0.03333333334 + 0.03333333334 + x = -0.000001 + 0.03333333334 Combine like terms: -0.03333333334 + 0.03333333334 = 0.00000000000 0.00000000000 + x = -0.000001 + 0.03333333334 x = -0.000001 + 0.03333333334 Combine like terms: -0.000001 + 0.03333333334 = 0.03333233334 x = 0.03333233334 Simplifying x = 0.03333233334Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03333433334, 0.03333233334}
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